In Patent Literature 1, the applicant of the present invention has previously disclosed 3DQ in which a high frequency quenching and a processing are carried out at the same time to a hollow workpiece made of steel having a closed cross section. FIG. 11 is a view showing a situation in which a bending member is produced by means of 3DQ with a processing apparatus 0.
As shown in FIG. 11, the processing apparatus 0 includes a transporting apparatus which is not shown, a supporting means 4, a high frequency induction heating apparatus 5, a water-cooling apparatus 6, and an articulated robot 7. Here, the transporting apparatus transports a long steel pipe 1 having a closed cross section in its longitudinal direction. That is, the steel pipe 1 is held by a holding unit 2, and transported in an axial direction (longitudinal direction) at a predetermined transporting speed by means of the transporting apparatus. The supporting means 4 movably holds the steel pipe 1 to be transported in the axial direction by the transporting apparatus. That is, the steel pipe 1 passes through an installation position of the support means 4 to be transported in the axial direction. The high frequency induction heating apparatus 5 partly heats the steel pipe 1 at a more downstream side in the transporting direction of the steel pipe 1 to be transported than the supporting means 4. This makes the steel pipe 1 partly and rapidly heated. The water-cooling apparatus 6 cools the heated portion at a more downstream side in the transporting direction of the steel pipe 1 than the high frequency induction heating apparatus 5. Since the steel pipe 1 is heated to a high temperature between the high frequency induction heating apparatus 5 and the water-cooling apparatus 6, its deformation resistance is largely decreased. Therefore, the heated portion of the steel pipe 1 heated by the high frequency induction heating apparatus 5 is rapidly cooled by the water-cooling apparatus 6. The articulated robot 7 moves in three-dimensional directions including at least the transporting direction of the steel pipe 1, at a more downstream side in the transporting direction of the steel pipe 1 than the water-cooling apparatus 6, while holding the steel pipe 1 to be transported with a holding means 7a. This adds a bending moment to the heated portion of the steel pipe 1 heated by the high frequency induction heating apparatus 5, whereby the metal material bends three dimensionally. By using the articulated robot 7, it is possible to movably hold the steel pipe 1 easily in three-dimensional directions including the transporting direction of the steel pipe 1.
Basically, the steel pipe 1 movably held in the axial direction by the articulated robot 7 is transported by the transporting apparatus from an upstream side to a downstream side, and at the downstream of the supporting means 4, for example a bending processing is carried out to the steel pipe 1, to thereby manufacture the bending member.
The steel pipe 1 is rapidly heated by the high frequency induction heating apparatus 5 arranged at the downstream side of the supporting means 4, to a temperature range with which the steel pipe 1 can be partly quenched. At the same time, the steel pipe 1 is rapidly cooled by the water-cooling apparatus 6 arranged at a downstream of the high frequency induction heating apparatus 5. Accordingly, a high-temperature portion (red heat portion) which moves in an axial direction being the opposite direction from the transporting direction of the steel pipe 1 is formed on the steel pipe 1. Then, the processing is carried out to the steel pipe 1, by moving the articulated robot 7 two dimensionally or three dimensionally while the steel pipe 1 is transported, to add for example a bending moment to the red heat portion.
In this regard, by adequately setting the heating temperature and cooling speed of the steel pipe 1, it is possible to quench the steel pipe 1. Therefore, according to 3DQ, it is possible to manufacture a lightweight bending member having a high intensity at high work efficiency.
FIG. 12 includes an explanation view showing a situation in which a high frequency quenching and a bending processing are simultaneously carried out by means of 3DQ, to a hollow steel workpiece 9 having a closed cross section and an outward flange 9a. FIG. 12A is a perspective view, and FIG. 12b is a cross-sectional view taken along the line C-C in FIG. 12A.
As shown in FIGS. 12A and 12B, if the workpiece 9 is tried to be heated uniformly in its circumferential direction by means of a normal high frequency induction heating apparatus 5 of a conventional technique arranged surrounding the whole circumference of the workpiece 9, it is not possible to heat the outward flange 9a of the workpiece 9. As described below, this comes from the penetration depth of an electromagnetic wave.
FIG. 13 includes an explanation view conceptually showing the reason why the outward flange 9a of the workpiece 9 is not heated. FIG. 13A shows flow directions of a coil current which flows in the high frequency induction heating coil 5 and an eddy current generated at a general portion 9b, in a case where the penetration depth of an electromagnetic wave at the general portion 9b where the outward flange 9a is excluded from the workpiece 9 is larger than the sheet thickness of the general portion 9b. FIG. 13B shows flow directions of the coil current and the eddy current in a case where the penetration depth of an electromagnetic wave at the outward flange 9a of the workpiece 9 is larger than the sheet thickness of the outward flange 9a. FIG. 13C shows flow directions of the coil current and the eddy current in a case where the penetration depth of an electromagnetic wave at the general portion 9b of the workpiece 9 is smaller than the sheet thickness of the general portion 9b. FIG. 13D shows flow directions of the coil current and the eddy current in a case where the penetration depth of an electromagnetic wave at the outward flange 9a of the workpiece 9 is smaller than the sheet thickness of the outward flange 9a. 
As shown in FIGS. 13A to 13D, the eddy current generated at the workpiece 9 by the induction heating flows in a manner to be along the current flow of the heating coil of the high frequency induction heating apparatus 5 which is shown by void arrows. In this case, as shown by A part in FIG. 13B, since the eddy current mutually cancels thereby scarcely flows at the outward flange 9a, the outward flange 9a is not heated. In order to prevent this, as shown by B part in FIG. 13D, it is needed to increase the frequency of the coil current to thereby make the penetration depth of an electromagnetic wave small, in order to heat the outward flange 9a by means of the eddy current only at the vicinity of its surface layer so that the eddy current is not mutually canceled. However, if the heating is carried out as above, as is obvious, the heating efficiency decreases because only the surface layer of the general portion 9b is heated as shown in FIG. 13C. Also if the penetration depth is too small, the heat generation amount becomes insufficient whereby heating itself becomes imperfect. Therefore, in a case where the normal high frequency induction heating apparatus 5 shown in FIG. 12 is used, it is appropriate that the frequency is set in a range with which the penetration depth becomes approximately same as to ½ of the sheet thickness of the outward flange 9a 
Here, the penetration depth δ (m) is calculated from Formula 2. The symbol μ in Formula 2 is a magnetic permeability, μ′ is a relative magnetic permeability, μ0 is a magnetic permeability in a vacuum state, ω is an angular frequency, f is the frequency, and σ is conductivity.
                              δ          ⁡                      (            m            )                          =                                            2                              ω                ⁢                                                                  ⁢                σμ                                              =                                                    2                                  2                  ⁢                  π                  ⁢                                                                          ⁢                  f                  ⁢                                                                          ⁢                                      σμ                    ′                                    ⁢                                      μ                    0                                                                        =                          503.3              ⁢                                                1                                      f                    ⁢                                                                                  ⁢                    σ                    ⁢                                                                                  ⁢                                          μ                      ′                                                                                                                              (        2        )            
In Formula 2, the penetration depth δ (m) of an electromagnetic wave becomes smaller as the frequency f is larger and the magnetic permeability μ or the conductivity σ is larger. A steel material is a ferromagnetic body having a relative magnetic permeability μ′ of around 100 to 1000 at a room temperature; however, since the steel material loses the magnetic property at a magnetic transformation temperature (around 780° C.), the relative magnetic permeability μ′ decreases to 1. That is, the penetration depth δ (m) also largely differs at the magnetic transformation temperature as a boundary.
FIG. 14 is a graph showing a relationship between the frequency and penetration depth of the current of the high frequency induction heating apparatus. In FIG. 14, in a case where the temperature is the magnetic transformation temperature or less, the relative magnetic permeability is 100 and the conductivity is 1×107 S/m, and in a case where the temperature is the magnetic transformation temperature or more, the relative magnetic property is 1 and the conductivity is 9×105 S/m.
In order to quench the steel workpiece by 3DQ, it is needed to heat the workpiece to the A3 point temperature (around 900° C.) or more at which the steel transforms to austenite, and the A3 point temperature is same as or higher than the magnetic transformation temperature. Therefore, when the high frequency quenching of the workpiece is carried out, it is needed to evaluate the penetration depth at a temperature of the magnetic transformation temperature or more. The graph of FIG. 14 shows that: in order to carry out a high frequency quenching to a flange having a sheet thickness of for example 1 mm, it is needed to use a frequency of 300 kHz or more with which the penetration depth becomes 1 mm or less, which is nearly same as the sheet thickness, for controlling mutual cancel of the eddy current.
However, when the heating target temperature is same in the high frequency induction heating, a power source having a higher power is needed as the frequency is larger. A high-output power source has drawbacks that its equipment cost is very expensive and operation cost also becomes expensive. Therefore, it is needed to develop a high frequency induction heating coil capable of heating a flange with a frequency with which the penetration depth at a temperature of the magnetic transformation temperature of the workpiece or more is same as or larger than the sheet thickness of the flange, by means of a low-output power source.
Patent Literature 2 discloses an invention of uniformly heating a workpiece having an outward flange, in its circumference direction by means of a high frequency induction heating coil having a shape offsetting in an axial direction of the workpiece along the outward flange of the workpiece.